Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol’skii–Besov spaces

2021 ◽  
Vol 252 (4) ◽  
pp. 508-525
Author(s):  
Anatolii Sergiiovych Romanyuk ◽  
Viktor Sergiiovych Romanyuk
Keyword(s):  
Besov Spaces ◽  
Best Approximation ◽  
The Best Approximation

Approximative characteristics and properties of operators of the best approximation of classes of functions from the Sobolev and Nikol'skii-Besov spaces

2020 ◽  
Vol 17 (3) ◽  
pp. 372-395
Author(s):  
Anatolii Romanyuk ◽  
Viktor Romanyuk
Keyword(s):  
Besov Spaces ◽  
Best Approximation ◽  
Linear Operators ◽  
Trigonometric Polynomials ◽  
Exact Order ◽  
Periodic Functions ◽  
Sobolev Classes ◽  
The Best Approximation ◽  
Several Variables

We have obtained the exact-order estimates for some approximative characteristics of the Sobolev classes $\mathbb{W}^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}$ and Nikоl'skii--Besov classes $\mathbb{B}^{\boldsymbol{r}}_{p,\theta}\ $ of periodic functions of one and several variables in the norm of the space $B_{\infty, 1}$. Properties of the linear operators realizing the orders of the best approximation for the classes $\mathbb{B}^{\boldsymbol{r}}_{\infty, \theta}$ in this space by trigonometric polynomials generated by a set of harmonics with $``$numbers$"$ from step hyperbolic crosses are investigated.

Intracranial volume-pressure relationship in man

1982 ◽  
Vol 56 (4) ◽  
pp. 524-528 ◽  
Author(s):  
Joseph Th. J. Tans ◽  
Dick C. J. Poortvliet
Keyword(s):  
Best Approximation ◽  
Continuous Monitoring ◽  
Fluid Pressure ◽  
Constant Term ◽  
Volume Index ◽  
Intracranial Volume ◽  
Content Type ◽  
The Best Approximation ◽  
Ventricular Fluid Pressure ◽  
Fine Print

✓ The pressure-volume index (PVI) was determined in 40 patients who underwent continuous monitoring of ventricular fluid pressure. The PVI value was calculated using different mathematical models. From the differences between these values, it is concluded that a monoexponential relationship with a constant term provides the best approximation of the PVI.

scholarly journals The best approximation and composition with inner functions.

1995 ◽  
Vol 42 (2) ◽  
pp. 367-378 ◽  
Author(s):  
M. Mateljević ◽  
M. Pavlović
Keyword(s):  
Best Approximation ◽  
Inner Functions ◽  
The Best Approximation

scholarly journals The Best Approximation of an Objective State With a Given Set of Quantum States

2021 ◽  
pp. 2100407
Author(s):  
Li‐qiang Zhang ◽  
Nan‐nan Zhou ◽  
Chang‐shui Yu
Keyword(s):  
Best Approximation ◽  
Quantum States ◽  
The Best Approximation ◽  
Objective State

scholarly journals On one approximation of flat curves by broken lines

2021 ◽  
Vol 15 ◽  
pp. 31
Author(s):  
S.V. Babenko ◽  
V.I. Ruban
Keyword(s):  
Best Approximation ◽  
The Best Approximation ◽  
Curve Approximation

We investigate the interrelations between the error of one method of curve approximation and the error of the best approximation.

Jurisdiction as Political Power

2020 ◽  
pp. 130-158
Author(s):  
Lea Raible
Keyword(s):  
Human Rights ◽  
Best Approximation ◽  
Political Power ◽  
Public Institutions ◽  
States Of Affairs ◽  
The Best Approximation

Moving from the conceptual to the substantive, this chapter refines our account of jurisdiction based on a concept of power and argues that it is best understood as political power in particular, as opposed to coercion. I argue that political power in this context should be conceptualised to denote the ability of public institutions to determine how individual powers are transformed. That is, political power is the ability of public institutions to mediate the abilities of individuals into a different set of abilities. As such, it is constitutive of and necessary for public institutions, it affects individuals because it provides the very framework for them to pursue their lives in equality, and it is virtually unavoidable. The exercise of political power results in non-exclusive control on particular states of affairs in the area of the rights outlined in any given treaty. The vehicle through which this power is manifested is the choice and application of rules. Political power so understood is the best approximation of a factual position to guarantee equality, which, as we have seen in Chapter 2, is what justifies human rights obligations of public institutions in the first place.

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